Why doesn't this simplify to True? More importantly, how can I get this to evaluate to True? I'm going through some manipulations of equations, and I'd like to use Mathematica to doublecheck my math and help with it.

I run into the same problem with Sum, where Integrate in the previous equation can be replaced by Sum. I'm using Mathematica 8.0.4.0.

I found that adding d[expression ,x] with Simplify or FullSimplify will evaluate to true. In other words, I am taking the derivative of the expression, and that seems to eliminate the integrals. I'd like to know if there are other workarounds, though. The new code is: FullSimplify[ D[Integrate[a[x] + b[x], x] == Integrate[a[x], x] + Integrate[b[x], x], x]]
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Matt GroffJul 15 '12 at 22:56

Why do you need any workarounds ? Your last issue with FullSimplify is just an inconsequence of M. Look at Integrate[a[x] + b[x], x], Integrate[a[x], x] and, all they return the results as the integrals would actually exist, moreover as they would be differentiable. While that is not correct in general.
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ArtesJul 16 '12 at 0:40

@Artes: I was just wondering if there are any related features available. What did you mean by M?
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Matt GroffJul 16 '12 at 2:03

M like Mathematica. I meant it wasn't a good feature of M when it returned True in that case. Look that you need not FullSimplify to get True, evaluate that expression without FullSimplify. It shouldn't return True, unless you assume a[x] to be integrable/ differentiable e.g. a[x_]:=x^2. There are many imperfect issues.
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ArtesJul 16 '12 at 2:14

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